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Fontaine-Mazur conjecture in the residually reducible case (I)

Lue Pan

University of Chicago

Thursday, February 14, 2019 - 1:25pm to 2:25pm

Vincent Hall 113

We prove the modularity of some two-dimensional residually reducible p-adic Galois representations over Q when p is at least 5. In the first talk, I will present a generalization of Emerton's local-global compatibility result. In the second talk, I will use this compatibility result to make a patching argument for completed homology in this setting.